Infinite-dimensional LMI approach to H<sup>∞</sup> control synthesis for linear systems with time delay

Abstract

This paper considers a synthesis problem of H<sup>∞</sup> controllers for linear systems with time delay in the form of delay-dependent memory state feedback, and develops a new Linear Matrix Inequalities (LMIs) approach. First, we present an existence condition and an explicit formula of H<sup>∞</sup> controllers in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of H<sup>∞</sup> controllers based on the finite-dimensional LMIs.

title = "Infinite-dimensional LMI approach to H∞ control synthesis for linear systems with time delay",

abstract = "This paper considers a synthesis problem of H∞ controllers for linear systems with time delay in the form of delay-dependent memory state feedback, and develops a new Linear Matrix Inequalities (LMIs) approach. First, we present an existence condition and an explicit formula of H∞ controllers in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of H∞ controllers based on the finite-dimensional LMIs.",

T1 - Infinite-dimensional LMI approach to H∞ control synthesis for linear systems with time delay

AU - Azuma, Takehito

AU - Ikeda, Kojiro

AU - Uchida, Kenko

PY - 2015/3/24

Y1 - 2015/3/24

N2 - This paper considers a synthesis problem of H∞ controllers for linear systems with time delay in the form of delay-dependent memory state feedback, and develops a new Linear Matrix Inequalities (LMIs) approach. First, we present an existence condition and an explicit formula of H∞ controllers in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of H∞ controllers based on the finite-dimensional LMIs.

AB - This paper considers a synthesis problem of H∞ controllers for linear systems with time delay in the form of delay-dependent memory state feedback, and develops a new Linear Matrix Inequalities (LMIs) approach. First, we present an existence condition and an explicit formula of H∞ controllers in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of H∞ controllers based on the finite-dimensional LMIs.